Contradictory are those that differ both in quantity and quality; as, every man is a living creature, some man is not a living-creature; which can neither be both true, nor both false.
Consequence, what it is.
18. A proposition is said to follow from two other propositions, when these being granted to be true, it cannot be denied but the other is true also. For example, let these two propositions, every man is a living creature, and, every living creature is a body, be supposed true, that is, that body is the name of every living creature, and living creature the name of every man. Seeing therefore, if these be understood to be true, it cannot be understood that body is not the name of every man, that is, that every man is a body is false, this proposition will be said to follow from those two, or to be necessarily inferred from them.
Falsity cannot follow from truth.
19. That a true proposition may follow from false propositions, may happen sometimes; but false from true, never. For if these, every man is a stone, and every stone is a living creature, (which are both false) be granted to be true, it is granted also that living creature is the name of every stone, and stone of every man, that is, that living creature is the name of every man; that is to say, this proposition every man is a living creature, is true, as it is indeed true. Wherefore a true proposition may sometimes follow from false. But if any two propositions be true, a false one can never follow from them. For if true follow from false, for this reason only, that the false are granted to be true, then truth from two truths granted will follow in the same manner.
How one proposition is the cause of another.
20. Now, seeing none but a true proposition will follow from true, and that the understanding of two propositions to be true, is the cause of understanding that also to be true which is deduced from them; the two antecedent propositions are commonly called the causes of the inferred proposition, or conclusion. And from hence it is that logicians say, the premises are causes of the conclusion; which may pass, though it be not properly spoken; for though understanding be the cause of understanding, yet speech is not the cause of speech. But when they say, the cause of the properties of any thing, is the thing itself, they speak absurdly. For example, if a figure be propounded which is triangular; seeing every triangle has all its angles together equal to two right angles, from whence it follows that all the angles of that figure are equal to two right angles, they say, for this reason, that that figure is the cause of that equality. But seeing the figure does not itself make its angles, and therefore cannot be said to be the efficient-cause, they call it the formal-cause; whereas indeed it is no cause at all; nor does the property of any figure follow the figure, but has its being at the same time with it; only the knowledge of the figure goes before the knowledge of the properties; and one knowledge is truly the cause of another knowledge, namely the efficient cause.
And thus much concerning proposition; which in the progress of philosophy is the first step, like the moving towards of one foot. By the due addition of another step I shall proceed to syllogism, and make a complete pace. Of which in the next chapter.